Details

Time bar (total: 18.5s)

sample88.0ms

Algorithm
intervals
Results
20.0ms43×body2560valid
15.0ms175×body80valid
12.0ms31×body1280valid
8.0ms106×body80nan
5.0ms18×body640valid
2.0ms4×body5120valid
1.0ms6×body320valid
1.0ms5×body160valid

simplify135.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
01217
12217
24216
38216
410416
511216
done11216

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 3.0 a) c)
0.8b
(- (* b b) (* (* 3.0 a) c))
1.4b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
24.7b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
22×*-un-lft-identity
20×add-cube-cbrt
19×prod-diff
16×sqrt-prod
10×pow1
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×fma-neg
4×expm1-log1p-u log1p-expm1-u
3×flip3-- associate-*r* pow-prod-down prod-exp flip-- cbrt-unprod
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative distribute-lft-out--
Counts
4 → 94
Calls
4 calls:
18.0ms
(* (* 3.0 a) c)
9.0ms
(- (* b b) (* (* 3.0 a) c))
79.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
22.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series323.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(* (* 3.0 a) c)
77.0ms
(- (* b b) (* (* 3.0 a) c))
129.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
95.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify4.3s

Counts
106 → 106
Iterations

Useful iterations: 3 (2.3s)

IterNodesCost
01611863
13671562
211281333
345171245
done50001245

prune406.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.4b

localize38.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
1.4b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
24.7b
(sqrt (- (* b b) (* (* 3.0 a) c)))
24.7b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite178.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
38×*-un-lft-identity
36×prod-diff
34×add-cube-cbrt
32×sqrt-prod
12×fma-neg
8×add-log-exp
6×pow1
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u difference-of-squares
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log distribute-lft-out--
Counts
4 → 116
Calls
4 calls:
53.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
89.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
12.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
20.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series477.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
125.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
120.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
116.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify3.4s

Counts
128 → 128
Iterations

Useful iterations: done (3.4s)

IterNodesCost
01132856
12682310
27181948
327111774
done50011674

prune538.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 13.4b

localize26.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
24.7b
(sqrt (- (* b b) (* (* 3.0 a) c)))
24.7b
(sqrt (- (* b b) (* (* 3.0 a) c)))
24.7b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
23×*-un-lft-identity
22×sqrt-prod
21×add-cube-cbrt
18×prod-diff
7×pow1
6×fma-neg sqrt-div add-log-exp
4×add-exp-log expm1-log1p-u flip3-- add-cbrt-cube flip-- log1p-expm1-u
3×rem-sqrt-square sqrt-pow1 pow1/2
2×difference-of-squares
1×sub-neg diff-log distribute-lft-out--
Counts
4 → 92
Calls
4 calls:
64.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
21.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
12.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
12.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series430.0ms

Counts
4 → 12
Calls
4 calls:
136.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
103.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
101.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
89.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify3.2s

Counts
104 → 104
Iterations

Useful iterations: done (3.2s)

IterNodesCost
01132042
12681675
27181476
327111387
done50011337

prune583.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 13.4b

localize45.0ms

Local error

Found 4 expressions with local error:

25.5b
(cbrt (- (* b b) (* (* 3.0 a) c)))
25.5b
(cbrt (- (* b b) (* (* 3.0 a) c)))
25.5b
(cbrt (- (* b b) (* (* 3.0 a) c)))
25.9b
(fma (sqrt (* (cbrt (- (* b b) (* (* 3.0 a) c))) (cbrt (- (* b b) (* (* 3.0 a) c))))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c)))) (- b))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×cbrt-div
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×flip3-- pow1/3 flip--
1×fma-udef
Counts
4 → 55
Calls
4 calls:
8.0ms
(cbrt (- (* b b) (* (* 3.0 a) c)))
6.0ms
(cbrt (- (* b b) (* (* 3.0 a) c)))
6.0ms
(cbrt (- (* b b) (* (* 3.0 a) c)))
0.0ms
(fma (sqrt (* (cbrt (- (* b b) (* (* 3.0 a) c))) (cbrt (- (* b b) (* (* 3.0 a) c))))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c)))) (- b))

series613.0ms

Counts
4 → 12
Calls
4 calls:
165.0ms
(cbrt (- (* b b) (* (* 3.0 a) c)))
143.0ms
(cbrt (- (* b b) (* (* 3.0 a) c)))
128.0ms
(cbrt (- (* b b) (* (* 3.0 a) c)))
176.0ms
(fma (sqrt (* (cbrt (- (* b b) (* (* 3.0 a) c))) (cbrt (- (* b b) (* (* 3.0 a) c))))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c)))) (- b))

simplify2.9s

Counts
67 → 67
Iterations

Useful iterations: done (2.9s)

IterNodesCost
0881442
11991258
25591121
320051103
done50011076

prune413.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 12.1b

regimes4.0ms